In this post, we focus on one of the most basic distinctions between different data types: . Quantitative research is expressed in numbers and graphs. Some common quantitative data collection methods include: Qualitative data is gathered through interviews, surveys, and observations. Levels of Measurement: Nominal, Ordinal, Interval and Ratio, Your email address will not be published. Through qualitative data, you can really gauge how people feel and why they take certain actionscrucial if youre running any kind of organization and want to understand how your target audience operates. Keywords: Qualitative research; Hierarchy of evidence; Quality indicators; Empirical studies; Qualitative evidence for clinical practice; Evidence-based medicine 1. The distance it is from your home to the nearest grocery store. All bottles of mustard produced in the plant in the given year. B. Moreover, businesses can use the numeric estimate to develop project management plans and contingency reserves. Do you want to understand something, such as a concept, experience, or opinions? A. Sage. However, our best friend example has hopefully made it easier for you to distinguish between quantitative and qualitative data. 1. If you want easy recruiting from a global pool of skilled candidates, were here to help. D. Bar Graph with Other/Unknown Category. For example, it does not make sense to find an average hair color or blood type. They are always numerical. Is the variable qualitative or quantitative? feet, and 210 sq. Amount of money (in dollars) won playing poker. Introduction to Statistics is our premier online video course that teaches you all of the topics covered in introductory statistics. The 1096 male university graduates who have a white collar job. The 1096 male university graduates who have a white collar job. Weights are quantitative continuous data because weights are measured. Quantitative. Determine whether the underlined value is a parameter or a statistic. feet, 180 sq. Quantitative vs qualitative data: What are they, and whats the difference between them? If it requires category, then it is qualitative. For example, a rating scale or closed questions on a questionnaire would generate quantitative data as these produce either numerical data or data that can be put into categories (e.g., yes, no answers). Qualitative data is collected by interviewing and observing. Doing quantitative research in the social sciences: An integrated approach to research design, measurement and statistics. C. The variable is quantitative because it is an attribute characteristic. Is the variable discrete or continuous? The aim of qualitative research is to understand the social reality of individuals, groups, and cultures as nearly as possible as its participants feel it or live it. Learn more about us. Research is used to test a theory and ultimately support or reject it. CareerFoundry is an online school for people looking to switch to a rewarding career in tech. Quantitative data is information about quantities, and therefore numbers, and qualitative data is descriptive, and regards phenomenon which can be observed but not measured, such as language. The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. The Pareto chart has the bars sorted from largest to smallest and is easier to read and interpret. Context: Quantitative experiments do not take place in natural settings. Quantitative data is generated by measuring or counting certain entities, or by performing calculations. Qualitative descriptions can be important in suggesting possible relationships, causes, effects, and dynamic processes. Operationalization means turning abstract conceptual ideas into measurable observations. Therefore, a qualitative researcher immerses her/himself in the field, in natural surroundings. document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); Statology is a site that makes learning statistics easy by explaining topics in simple and straightforward ways. Identify your skills, refine your portfolio, and attract the right employers. The colors red, black, black, green, and gray are, 1.1: Definitions of Statistics and Key Terms, http://cnx.org/contents/30189442-6998-4686-ac05-ed152b91b9de@17.44, http://cnx.org/contents/30189442-6992b91b9de@17.44, status page at https://status.libretexts.org. Area of a park If youre considering a career in data, youll find links to some useful articles at the end of this post. This also affects the ability to generalize study findings to wider populations. high school, Associates degree, Bachelors degree), Marital status (e.g. C. Scribbr. Figure 3. Quantitative data may be either discrete or continuous. Lets do that now, starting with quantitative data. It is subjective and exists only in reference to the observer. June 12, 2020 answer choices. While, theoretically, an infinite number of people could live in the house, the number will always be a distinct value, i.e. Distance between sides of a street You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Our graduates come from all walks of life. Answer (1 of 4): Not all streets have numbers, but what you might need is the building number on that named street. Qualitative data are generally described by words or letters. It can be used to generate hypotheses and theories from the data. For the quantitative researcher, the reality is objective, exists separately from the researcher, and can be seen by anyone. The strengths and weaknesses of quantitative and qualitative research: what method for nursing? Yet numbers are integral to qualitative research, as meaning depends, in part, on number. Bhandari, P. Labels and categories used in surveys and questionnaires, e.g. The study can be reproduced in other cultural settings, times or with different groups of participants. Is the variable qualitative or quantitative? Number of street corner mailboxes in the city of Philadelphia. The study's design evolves during the research and can be adjusted or changed as it progresses. Quantitative researchers aim to establish general laws of behavior and phenomenon across different settings/contexts. What it really boils down to, in very simple terms, is that quantitative data is countable or measurable, relating to numbers, while qualitative data is descriptive, relating to language. For those that are defined, give the size of the resulting matrix. Indicate whether quantitative data are continuous or discrete. . Examples could include customer satisfaction surveys, pizza toppings, peoples favorite brands, and so on. Quantitative research is the opposite of qualitative research, which involves collecting and analyzing non-numerical data (e.g., text, video, or audio). The field of program evaluation, critical for social policy development, often has not adequately embraced the full range of methodological tools needed to understand and capture the complexity of these . Qualitative data are primarily descriptive, tending to represent peoples opinions or experiences. For more introductory posts, you should also check out the following: Standard deviation vs standard error: Whats the difference? The term 'qualitative' refers to anything which can be observed but not counted or measured. Qualitative and quantitative studies, excluding review articles and meta-analyses, will be eligible, without date restrictions. blue, green, brown), Breed of dog (e.g. Qualitative vs. Quantitative Variables: What's the Difference? Unlike quantitative data, qualitative data cannot be measured or counted. While discrete variables are always fixed, this doesnt necessarily mean theyre always whole numbers. Confirmation bias: The researcher might miss observing phenomena because of focus on theory or hypothesis testing rather than on the theory of hypothesis generation. Examples include: Number of students in a class Number of square feet in a house Population size of a city Their values may occur more than once for a set of data. However, in most cases, the street number is the number describing where a building is located on a street. C. Of all the ways in which statisticians classify data, one of the most fundamental distinctions is that between qualitative and quantitative data. This means that qualitative researchers study things in their natural settings, attempting to make sense of, or interpret, phenomena in terms of the meanings people bring to them. Events can be understood adequately only if they are seen in context. The primary outcome, actigraphic . As weve seen, the distinction is not that tricky, but its important to get right. This is relevant for our current topic because, while discrete and continuous variables are distinct from each other, they are, , you can put qualitative data out of your mind for now. Braun, V. & Clarke, V. (2006). and measures of time, height, distance, volume, mass (and so on) are all types of quantitative data. cars that are blue, red, green, and so on). The main differences between quantitative and qualitative data lie in what they tell us, how they are collected, and how they are analyzed. Hint: Data that are discrete often start with the words the number of., [reveal-answer q=237625]Show Answer[/reveal-answer] [hidden-answer a=237625]Items a, e, f, k, and l are quantitative discrete; items d, j, and n are quantitative continuous; items b, c, g, h, i, and m are qualitative.[/hidden-answer]. Quantitative Research. Quantitative data tells us how many, how much, or how often (e.g. The studys design evolves during the research and can be adjusted or changed as it progresses. Qualitative data is descriptive, relating to language. Then you might describe some of their most prominent personality traits. Well outline the main advantages and disadvantages of each now. These types of data are generally collected through interviews and observations. Given that qualitative data cannot be measured objectively, it is open to subjective interpretation and therefore requires a different approach to analysis. With qualitative data analysis, the focus is on making sense of unstructured data (such as large bodies of text). The variable is continuous because it is not countable. Quantitative data refers to anything that can be counted or measured. Whats the difference between covariance and correlation? 2003-2023 Chegg Inc. All rights reserved. Qualitative methods allow you to explore concepts and experiences in more detail. Want to skip ahead to a specific section? Findings are, therefore, likely to be context-bound and simply a reflection of the assumptions that the researcher brings to the investigation. Next, you perform inferential statistics to test your hypothesis. A. Despite standardized procedures, structural biases can still affect quantitative research. The variable is qualitative because it is an attribute characteristic. Saul Mcleod, Ph.D., is a qualified psychology teacher with over 18 years experience of working in further and higher education. My best friend is 5 feet and 7 inches tall, My best friend has one older sibling and two younger siblings, My best friend lives twenty miles away from me, My best friend is funny, loud, and a good listener, They can also be quite impatient and impulsive at times, They have a very friendly face and a contagious laugh, Measurements such as height, length, and weight, Counts, such as the number of website visitors, sales, or email sign-ups, Projections, such as predicted sales or projected revenue increase expressed as a percentage, Quantification of qualitative datafor example, asking customers to rate their satisfaction on a scale of 1-5 and then coming up with an overall customer satisfaction score, Interview transcripts or audio recordings, The text included in an email or social media post, Product reviews and customer testimonials, Observations and descriptions; e.g. Can be counted in whole numbers, but cannot be measured. | Definition, Uses & Methods. Discrete or Continuous 1. street number 2. phone number 3. gross annual income 4. housing cost 1 See answer Advertisement Advertisement renalyndomingo24 renalyndomingo24 Answer: 1. discrete. It is always numerical in nature. They are always numerical. These are data that can be counted, but not measured. This type of data can be collected using diary accounts or in-depth interviews and analyzed using grounded theory or thematic analysis. This allows the respondent to talk in some depth, choosing their own words. feet. Quantitative research is the process of collecting and analyzing numerical data. Hopefully by now, you can tell the difference between discrete and continuous variables. Small letters like x or y generally are used to represent data values. November 24, 2022. Quantitative data is either discrete or continuous: Some everyday examples of quantitative data include: Qualitative data may be classified as nominal or ordinal: Nominal and ordinal data tends to come up within the context of conducting questionnaires and surveys. Useful for testing and validating already constructed theories. The variable is discrete because it is countable. The researcher does not just leave the field with mountains of empirical data and then easily write up his or her findings. January 14. lab, bulldog, poodle), Level of education (e.g. Throughout this post, weve defined quantitative and qualitative data and explained how they differ. In this situation, create a bar graph and not a pie chart. To illustrate this, lets once again consider the dataset from the previous example: For the quantiative variable Seasons Played, we can calculate the following metrics: These metrics give us a good idea of where the center value is located as well as how spread out the values are for this variable. Then, you can use statistical analysis to answer your research questions. Now we have a rough idea of the key differences between discrete vs continuous variables, lets look at some solid examples of the two. We can use statistics to summarize our data, describing patterns, relationships, and connections. The variable is continuous because it is not countable. A. Although some of these Quantitative data is suitable for statistical analysis and mathematical calculations, while qualitative data is usually analyzed by grouping it into meaningful categories or themes. Is the variable discrete or continuous? Quantitative Variables: Sometimes referred to as "numeric" variables, these are variables that represent a measurable quantity. All bottles of mustard produced in the plant on January 14. Interest in qualitative data came about as the result of the dissatisfaction of some psychologists (e.g., Carl Rogers) with the scientific study of psychologists such as behaviorists (e.g., Skinner ). For example, a childs birth weight can be measured to within a single gram or to within 10 grams. C. What is the demographic makeup of Singapore in 2020? At the same time, quantitative data is objective; its less susceptible to bias than qualitative data, which makes it easier to draw reliable and generalizable conclusions. qualitative or quantitative data is not a valid basis for distin-guishing qualitative from quantitative research, stating that "the contrast between words and numbers does not get us very far" (p. 162). This is probably because it can be categorized into separate groups, (e.g. Score in a Math Quiz3. On top of that, you could describe how many siblings and pets they have, where they live, and how often they go swimming (their favorite hobby). Have fixed values, with clear spaces between them. Results can be compared statistically. Determine whether the quantitative variable is discrete or continuous. The variable is qualitative because it is an attribute characteristic. Theyll provide feedback, support, and advice as you build your new career. Interpreting quantitative data with SPSS. The main disadvantage of quantitative data is that it can lack depth and context. Originally from England, Emily moved to Berlin after studying French and German at university. The variable is continuous because it is not countable. Notice that qualitative data could be much more than just words or text. Experts are tested by Chegg as specialists in their subject area. Journal of advanced nursing, 20(4), 716-721. C. Quantitative methods allow you to systematically measure variables and test hypotheses. married, single, divorced), We can use many different metrics to summarize, However, we can only use frequency tables and relative frequency tables to summarize, How to Calculate a Pooled Standard Deviation (With Example). The point is, you can potentially measure the weight with ever-increasing degrees of accuracy because the measurement scale is continuous. Quantitative research involves the process of objectively collecting and analyzing numerical data to describe, predict, or control variables of interest. you cannot have 2.4 of a person living in a house. B. Our career-change programs are designed to take you from beginner to pro in your tech careerwith personalized support every step of the way. The 1096 male university graduates who have received a raise at work. Revised on Because of the time and costs involved, qualitative designs do not generally draw samples from large-scale data sets. Perhaps you want to know how a user feels about a particular product; again, qualitative data can provide such insights. Tamang sagot sa tanong: Assessment A. Classify the following as Qualitative or Quantitative. Well then explore all the key ways in which they differfrom how they are collected and analyzed, to the advantages and disadvantages of each. Using inferential statistics, you can make predictions or generalizations based on your data. Whether you plan to create a quantitative survey, a qualitative survey, or a combination of the two, SurveyLegend has you covered! 28. Quantitative Information - Involves a measurable quantitynumbers are used. A street number is usually a precise location of a particular building or a house in the street. However, as a growing number of education scholars engaged in critical approaches to quantitative inquiry, instances of conflation began to surface. Descriptive vs. Inferential Statistics like histograms or line charts, which are excellent for highlighting trends or patterns in data measured over time. If you want to cite this source, you can copy and paste the citation or click the Cite this Scribbr article button to automatically add the citation to our free Citation Generator. First, you use descriptive statistics to get a summary of the data. (2009), and many of the contributors to a volume edited by Bergman A good example of a qualitative research method would be unstructured interviews which generate qualitative data through the use of open questions. Measuring angles in radians might result in such numbers as , and so on. Quantitative Variables - Variables whose values result from counting or measuring something. by D. Carr, L. T. (1994). Determine whether the variable is qualitative or quantitative. Both types of quantitative data, well recap this before kicking off. Denscombe, M. (2010). For the given exercise determine whether the given matrix expression is defined. The data are the number of books students carry in their backpacks. Lets summarize the key differences before exploring each aspect in more detail: To illustrate the difference between quantitative and qualitative data, lets use an example. Examples include: 2. Qualitative Quantitative Researchers often prefer to use quantitative data over qualitative data because it lends itself more easily to mathematical analysis. Understanding the difference between quantitative and qualitative data is one of the very first steps towards becoming a data expert. To learn more about the importance of statistics in data analytics, try out afree introductory data analytics short course. [reveal-answer q=935468]Show Answer[/reveal-answer] [hidden-answer a=935468]This pie chart shows the students in each year, which is qualitative data. Statistical analysis can be used to identify trends in the data, to establish if theres any kind of relationship between a set of variables (e.g. 2023 Simply Psychology - Study Guides for Psychology Students, test causal relationships between variables, The strengths and weaknesses of quantitative and qualitative research, Introduction to quantitative and qualitative research. Take part in one of our FREE live online data analytics events with industry experts, and read about Azadehs journey from school teacher to data analyst. 3. continuous. Collaborative Exercise 1.2. Checklist: discrete vs continuous variables. Analysis of qualitative data is difficult, and expert knowledge of an area is necessary to try to interpret qualitative data. The biggest advantage of qualitative data is that it offers rich, in-depth insights and allows you to explore the context surrounding a given topic. In fields like data analytics and data science, which often require advanced math, its vital to understand the nature, structure, and characteristics of any dataset youre working with. In-Depth Interviewing: Researching People. In statistics, there are two types of variables: 1. Youve probably heard of discrete vs continuous data. For example, it does not make sense to find an average hair color or blood type. It can be used to find patterns and averages, make predictions, test causal relationships, and generalize results to wider populations. Here, well discuss which projects are better suited to which data. Temperature at Baguio City4. More accurately, they should be described as, In general, continuous data is best represented using. Small-scale quantitative studies may be less reliable because of the low quantity of data (Denscombe, 2010). If you want easy recruiting from a global pool of skilled candidates, were here to help. Both research types require raw data; Both are used to measure results; Sometimes one type of research complements the other. And for the qualitative variablePosition, we can create a frequency table to describe how often different values occur: This table lets us quickly see how frequently each position (G=guard, F=forward, C=center) occurred in the dataset. the type of car you drive. Experimental methods limit how a research participant can react to and express appropriate social behavior. McGraw Hill. However, other research methods, such as controlled observations and questionnaires, can produce both quantitative information. The variable is qualitative because it is an attribute characteristic. Again, you sample the same five students. What defines them as discrete is that there is a clear and consistent leap between variables and that these gaps dont take into account the difference. However, this is an inaccurate description because you cannot carry out mathematical functions on qualitative data. The variable is continuous because it is not countable. You may benefit from a mixed methods approach to data collection. Quantitative researchers try to control extraneous variables by conducting their studies in the lab. Q. Huston (2005), Sandelowski et al. number of Grade 7 students5. Indicate whether quantitative data are continuous or discrete. Qualitative data is defined as non-numerical data, such as text, video, photographs, or audio recordings. Two students carry three books, one student carries four books, one student carries two books, and one student carries one book. A. However, qualitative data is not just limited to labels and categories; it also includes unstructured data such as what people say in an interview, what they write in a product review, or what they post on social media. To collect quantitative data, you will often need to use operational definitions that translate abstract concepts (e.g., mood) into observable and quantifiable measures (e.g., self-ratings of feelings and energy levels). Similarities between qualitative and quantitative research. Take part in one of our FREE live online data analytics events with industry experts, and read about Azadehs journey from school teacher to data analyst. Research following a qualitative approach is exploratory and seeks to explain how and why a particular phenomenon, or behavior, operates as it does in a particular context. Researcher expertise: Poor knowledge of the application of the statistical analysis may negatively affect analysis and subsequent interpretation (Black, 1999). Research must be empirically based; therefore, it has traditionally been seen to reside in the domain of the theorist or expert. How has the average temperature changed globally over the last century? The Other/Unknown category is large compared to some of the other categories (Native American, 0.6%, Pacific Islander 1.0%). Nurture your inner tech pro with personalized guidance from not one, but two industry experts. Simply Scholar Ltd. 20-22 Wenlock Road, London N1 7GU, 2023 Simply Scholar, Ltd. All rights reserved. Our graduates are highly skilled, motivated, and prepared for impactful careers in tech. Build a career you love with 1:1 help from a career specialist who knows the job market in your area! Hypotheses can also be tested because of the use of statistical analysis (Antonius, 2003). depends on the data analytics project youre undertaking. Each type of data comes with advantages and disadvantages, and its important to bear these in mind when conducting any kind of research or sourcing data for analysis. Are you taking on research? SSS number 5. Doing so helps you determine the best statistical techniques to apply (e.g. A qualitative variable is a variable whose values are varied by attributes or characteristics. You compare self-ratings of procrastination behaviors between the groups after the intervention. Housing cost 1 See answer Advertisement . The variable is qualitative because it is a numerical measure. Book: Elementary Statistical Methods (Importer-error-Incomplete-Lumen), { "01.1:_Chapter_1" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "01.1:_Definitions_of_Statistics_and_Key_Terms" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "01.2:_Data:_Quantitative_Data_&_Qualitative_Data" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "01.3:_Sampling" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "01.4:_Levels_of_Measurement" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "01.5:_Frequency_&_Frequency_Tables" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "01.6:_Experimental_Design_&_Ethics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, { "00:_Front_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "01:_Main_Body" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "02:_Sampling_and_Data" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "03:_Descriptive_Statistics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "04:_Probability" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "05:_Discrete_Random_Variables" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "06:_Normal_Distribution" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "07:_The_Central_Limit_Theorem" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "08:_Confidence_Intervals" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "09:_Hypothesis_Testing_With_One_Sample" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "10:_Linear_Regression_and_Correlation" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "zz:_Back_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, 1.2: Data: Quantitative Data & Qualitative Data, https://stats.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fstats.libretexts.org%2F%3Ftitle%3DCourses%2FLumen_Learning%2FBook%3A_Elementary_Statistical_Methods_(Importer-error-Incomplete-Lumen)%2F01%3A_Main_Body%2F01.2%3A_Data%3A_Quantitative_Data_%2526_Qualitative_Data, \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}}}\) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\), The data are the colors of backpacks.